the distribution of the number of hours that a random sample of people spend doing chores per week is shown…

the distribution of the number of hours that a random sample of people spend doing chores per week is shown in the pie chart. use 32 as the midpoint for \30+ hours\. make a frequency distribution for the data. then use the table to estimate the sample mean and the sample standard deviation of the data set. click the icon to view the pie chart. first construct the frequency distribution. class frequency, f 0 - 4 6 5 - 9 12 10 - 14 23 15 - 19 18 20 - 24 16 25 - 29 13 30+ 4 find an approximation for the sample mean. $\bar{x}=square$ (type an integer or decimal rounded to the nearest tenth as needed.)

the distribution of the number of hours that a random sample of people spend doing chores per week is shown in the pie chart. use 32 as the midpoint for \30+ hours\. make a frequency distribution for the data. then use the table to estimate the sample mean and the sample standard deviation of the data set. click the icon to view the pie chart. first construct the frequency distribution. class frequency, f 0 - 4 6 5 - 9 12 10 - 14 23 15 - 19 18 20 - 24 16 25 - 29 13 30+ 4 find an approximation for the sample mean. $\bar{x}=square$ (type an integer or decimal rounded to the nearest tenth as needed.)

Answer

Explanation:

Step1: Find mid - points of each class

For class $0 - 4$, mid - point $x_1=\frac{0 + 4}{2}=2$; for $5 - 9$, $x_2=\frac{5+9}{2}=7$; for $10 - 14$, $x_3=\frac{10 + 14}{2}=12$; for $15 - 19$, $x_4=\frac{15+19}{2}=17$; for $20 - 24$, $x_5=\frac{20 + 24}{2}=22$; for $25 - 29$, $x_6=\frac{25+29}{2}=27$; for $30+$, $x_7 = 32$.

Step2: Calculate the product of mid - point and frequency for each class

$x_1f_1=2\times6 = 12$; $x_2f_2=7\times12=84$; $x_3f_3=12\times23 = 276$; $x_4f_4=17\times18=306$; $x_5f_5=22\times16 = 352$; $x_6f_6=27\times13=351$; $x_7f_7=32\times4 = 128$.

Step3: Calculate the sum of frequencies

$\sum f=6 + 12+23+18+16+13+4=92$.

Step4: Calculate the sum of the products

$\sum x_if_i=12 + 84+276+306+352+351+128=1509$.

Step5: Calculate the sample mean

The formula for the sample mean $\bar{x}=\frac{\sum x_if_i}{\sum f}$. So, $\bar{x}=\frac{1509}{92}\approx16.4$.

Answer:

$16.4$